quantum number

n is a positive integer, but is often represented as K, L, M, and so on, corresponding to 1, 2, 3, etc respectively. This represents the principal quantum number which is sometimes referred to as an energy level (such as it is later in this writeup).

l relates to the quantization of the orbitalangular momentum. It is an integer as well, between 0 and n-1. When it is 0, the state is s, a spherical shell with no net angular momentum. When l is 1, the state is p. In this case, there is directionality, a sort of dumbell shape elongated on the coordinate axes. If l is 2, the state is referred to as d. For more details on this see d orbital. The letter f corresponds to 3, see f orbital.

m There are two different m variables. mi is greater than -l and less than +l. ( -l <= mi <= l) and it reprsesnts the magnetic quantum number. ms however is either 1/2 or -1/2 indicating an "upward" or "downward" spin. It is called the "spin quantum number"

The Pauli Exclusion Principle says that no given electron in an atom can share exactly the same values of all four numbers with another. At least one must be different.

This information was adapted from my Materials Science and Engineering lecture notes.